Electronic excitations in transition metal dichalcogenide monolayers from an LDA plus GdW approach

Monolayers of transition metal dichalcogenides (TMDCs) have unique optoelectronic properties. Density functional theory allows only for a limited description of the electronic excitation energies in these systems, while a more advanced treatment within many-body perturbation theory employing the $\mathit{GW}/\mathrm{BSE}$ approximation is often rather time consuming. Here, we show that the recently developed $\mathrm{LDA}+\mathit{GdW}$ approach provides an efficient and at the same time reliable description of one-particle energies, as well as optical properties including bound excitons in TMDCs. For five exemplary materials (${\mathrm{MoSe}}_{2}, {\mathrm{MoS}}_{2}, {\mathrm{WSe}}_{2}, {\mathrm{WS}}_{2}$, and ${\mathrm{ReSe}}_{2}$), we discuss the numerical convergence, in particular with respect to k-point sampling, and show that the $\mathit{GdW}/\mathrm{BSE}$ approximation gives results similar to common $\mathit{GW}/\mathrm{BSE}$ calculations. Such efficient approaches are essential to treat larger multilayer systems or defects.